Derivation Atlas

An absolute background tick T alongside laboratory proper time tau, related by a smooth positive lapse.

An inverse-square endurance flux that becomes Newtonian gravity in the IR; micro-length identified with the Planck length.

A uniform creation/source rate (White-Void / BLOP events) mimicking a cosmological-constant term.

An internal S1 dial at every address; the quarter-turn generator J (J^2=-1) is what the textbook imaginary unit i was packaging.

A world-cell address is one completed modular-capacity event, not a primitive coordinate-lattice site. Discreteness is earned by completion.

Per-address ceilings on energy, power, and action; no infinite local alphabet at one completed event.

Every physical record closes one full 2-pi modular budget through a visible plus same-universe hidden completion.

Source equation closed: the QTT-native object is one diameter-\(\ell_A\) spherical pixellate support, the complete 24-state proper signed-permutation frame fibre, and one completed address stride form a product-capacity measure, \(\Delta V_A^{(4)}=24(\pi\ell_A^3/6)\ell_A=4\pi\ell_A^4\), with \(E_*=\rho_A^{(4)}\Delta V_A^{(4)}\). One member through one stride is only \(\delta V_{{\rm pix},A}^{(4)}=(\pi/6)\ell_A^4\); confusing the two creates a factor-of-24 type error.

\(E_P=m_Pc^2=\hbar\omega_P=\rho_{(4)}(4\pi\ell_P^4)\): mass, frequency, and four-density as four faces of one endpoint capacity. The fourth face inherits the finite QTT completed-event owner theorem above; \(4\pi\ell_P^4\) is not merely selected for dimensional correctness.

A finite-address source/readout theorem: every laboratory number is an access image of a completed source object. The independently constructed central effect \(A_w(\mathfrak L)\) is positive, becomes the original central projector in the sharp limit, and enters both the work ceiling and the Access-Law uncertainty floor without being inferred from either observed residual.

Separates six questions that a single green label cannot answer: equation closure, constructor closure, dimensional-anchor use, public chronology, empirical status, and scope. For every headline object X, Version 3.0 prints the eight-field card P(X)=(S_X,D_X,L_X,A_X,J_X,C_X,E_X,F_X): source word, constructor domain, logical load, dimensional anchor, forbidden-target Jacobian, chronology, empirical status, and falsifier. The static no-smuggling condition J_X^stat=0 is necessary but does not prove historical blindness; public chronology independently decides whether a landing is prospective or retrospective. Seven cards are closed for rho, q_H, R_H^EW, lambda_gamma, alpha_QTT^-1, the G-G_F bridge, and chi_g=1. The alpha landing remains a retrospective consistency audit, the G bridge remains an anchored Class-A audit, K2 remains source-open, and chi_g=1 remains a sealed Tier-K physical hypothesis after the no-go theorem. Shared upstream rails are printed, so correlated agreements cannot be multiplied into false independent significance. In the photon-edge word, 24 is the Artian Geometry A5-X completed pixellate-bundle source count; it is not imported from cubic symmetry and is not chosen from a laboratory target. The machine receipt passes 63 of 63 checks without retuning a source branch.

Unifies the thermodynamic, cosmological, measurement, fixed-origin source-volume, radiative, quantum-time, delayed-choice, twin-clock, and gravitational-clock arrows as typed readouts of one source-time orientation. The corrected ledger assigns completed-record order and persistence to A1/A7, keeps A2 endurance support and A3 source-volume production separate. Under the explicit fixed-origin premise B=M/m_A, the latter obeys N_SQ^A2=BN_T and N_SQ^A3=12BN_T(N_T+1). The time framework then uses the positive laboratory clock factor dt_lab = I_clk F_A3 exp(-E_A2) sqrt(1-v^2/c^2)dT, Quantized Now as Now_R(T_n)={X in R: a(X)=n}, the Time Tilt plus Creation Drift bridge theta_age=pi/8+pi/48=7pi/48 with t0_lab=T0_ABC cos(7pi/48), the A2 proper-time metric shadow d tau=exp(-E_A2)sqrt(1-v^2/c^2)dT, weak-field and Schwarzschild clock readouts, the quantized Lorentz boost ledger p_{n+1}=p_n+N_n M_* c, the high-regime twin address-tick sum, the no-past-rewrite boundary, and the closed retarded address operator G_phys^QTT=G_J^+=Theta_w L_J^-1 with Pi_phys G_J^- Pi_src=0. Full A2 infrared field dynamics are tracked in the A2 Einstein-field node; first-tick closure, deeper orientation derivation, high-regime clock tests, and direct w-address timing tomography remain future rows.

Defines the carrier-independent activation layer required before any reference-switch apparatus may call one history T-star and another tau. A candidate T-star terminal requires a completed source event C_E, continuous physical memory of that event, Xi_L<=epsilon_L, Xi_S>=eta_S, no later laboratory overwrite, one final basis-selecting readout, a uniquely ranked physical write ancestry, and a target-blind camera. Ordinary free evolution, software labels, detector clicks, and deliberately programmed pi/8 or CHSH geometry do not create a source terminal. Fifteen frozen gates compute G_PT. If G_PT=0, the only legal outcome is INELIGIBLE_NO_THEORY_VERDICT. If G_PT=1, the ordinary fixed point is R_clk=1 and the QTT-A1 fixed point is cos(pi/8)^q, with the detector degree q certified before target-bearing data are opened. The constructor is closed; platform qualification and empirical A1 judgment remain pending.

Separates the standard clock carrier Delta phi_clock=omega_0 Delta tau from a narrower A1 terminal-reference claim. One delocalized atomic clock must realize four physical terminal histories a,b in {tau,T}, retain the reversal-paired first clock-coherence phasors Z_ab^(+/-), and certify an ordinary cross-history map before target-bearing data are opened. The sealed statistic is R_qc,clk=[1/N_cross^ordinary] sqrt(D_tauT D_Ttau/(D_tautau D_TT)), with ordinary target 1 and QTT-A1 target cos(pi/8). The fixed separation is 7.6120467 percent; sigma(R)<=0.0152241 is the bare five-sigma requirement and 0.005 is the recommended laboratory goal. Three adversarial audits close carrier substitution, software-only terminal labels, target-derived transfer, pi/8/pi/4/CHSH programming, readout-exponent, covariance, and power traps. Synthetic recovery certifies the analysis path only; no physical four-terminal clock packet has yet been measured.

Replaces retrospective anomaly relabelling with a prospective physical graph: one continuously phase-connected T-candidate link and one physically clock-gated and reacquired tau-candidate link propagate simultaneously, each route is repeated after crossing the electronics roles, and at least two nondegenerate route orientations are required. The adversarial rank theorem uses (Omega_E x r).v=Omega_E.(r x v): on one central-force flyby this geometry term is nearly constant and a free inter-link offset absorbs it, so one route is ineligible. The eligible estimator is kappa_A1=(g^T C^-1 P_perp d)/(g^T C^-1 P_perp g), with ordinary target 0 and QTT-A1 target 1. The geometry coefficient is frozen, not fitted; sign and unit coefficient must transfer to held-out routes. Historical Anderson-type flyby anomalies and public tracking archives do not contain this crossed physical graph and receive no A1 verdict.

Norm preservation makes the history weight orthogonal; ledger additivity under history composition makes it a one-parameter group; A7 dial closure makes it 2-pi periodic. The surviving laboratory weight is the real J-rotor R_J(theta) = cos(theta) I + sin(theta) J. Positive scalar weights cannot interfere, so interference is a closure theorem, not an added quantum axiom.

A short-time completed-history kernel carries a capacity-fixed magnitude and a J-rotor phase R_J(Delta S/hbar - d pi/4). Tick composition plus ledger additivity produces K = integral D_A6 x · R_J(S[x]/hbar). The textbook integral over exp(iS/hbar) is the complex-coordinate shorthand of this real-dial finite path sum; the A6 support is part of the object, not decoration.

In the macroscopic regime |S|/hbar >> 1, neighboring non-stationary histories rotate through rapidly changing J-angles and cancel. Coherent laboratory survival therefore selects delta S_tot = 0. QTT's content is upstream of the standard stationary-phase theorem: it derives the rotor weight and the S/hbar angle, while the final cancellation step is established mathematics. A7U keeps variations closure-preserving across the visible-plus-hidden bundle.

On the primitive two-state completed-event face, every self-adjoint source generator that respects the event exchange symmetry is, modulo an irrelevant identity term, proportional to the swap direction S_e. The direction is therefore unique. The local source premises do not fix the dimensionless magnitude C_H: the full family H = E_*[(1-C_H/2)I+(C_H/2)S_e], with 0 < C_H ≤ 1, remains legal. The paper proves this magnitude no-go, separates a Hamiltonian matrix element from a transition probability, and defines the record-spend quotient that forbids counting the same completed event twice. C_H = 1 follows only conditionally when the global one-action allocation identity is added; that closure gate remains explicitly amber.

Integrating d theta = dS/hbar around one completed J-dial circle gives Delta S = 2 pi hbar = h. In QTT, hbar is action per radian of the real dial, and h is the cost of closing the dial once. The action quantum is not a separate smallest-action postulate; it is the closure of the dial.

One closure law gives four textbook projections: Planck-Einstein ET = h as the time circle, de Broglie p lambda = h as the space circle, Bohr-Sommerfeld integral p dq = n h as the phase-space loop, and flux quantization q Phi = n h as the gauge-holonomy loop. These are exact identity recoveries, so the node carries no sigma row.

The steady isotropic solution of the A2 endurance flux gives an inverse-square force in the infrared limit.

A positive finite operator counts funded completed-event classes once. Its A1 free-branch spectral curvature fixes inertial response; the weak-lapse expansion fixes passive response; A2 supplies the active source readout. Thus one eigenvalue gives active, passive, and inertial mass, while F = ma is the low-velocity laboratory shadow. A6+A7 fix admissibility and per-address capacity but do not, by themselves, populate the complete particle-mass spectrum.

Hamilton's principle and the path integral as the stationary real-dial phase over completed-address paths; the action quantum is h-bar per completed event.

Mass-energy equivalence read off the endurance ledger with c as a primitive carrier speed, not from boost algebra.

gamma = (1-v^2/c^2)^{-1/2} emerges from fixed-norm sharing of tick speed between hidden and visible cells, regularizing the v->c divergence.

Source action as a finite ledger over completed A5-X events; the laboratory Lagrangian and least-action integral are Access-Law images of that source ledger, not the constructor of it.

The imaginary unit is the laboratory shadow of the real-dial generator J. Phases, commutators, and path weights are real finite quarter-turns.

The first-order time law as address projection of the real-dial evolution; i d/dt psi = H psi is the lab packaging of J-native transport.

The quadratic real-J address capacity is unique in the declared finite additive symmetry class. Its identification with long-run frequency, and the fixed-address trace representation, require separately printed statistical and effect-functional premises.

Spin quantization and the spinor half-angle from the adjoint action of the real J-dial; the 720-degree return is a rotor theorem.

E = h-bar omega and p = h-bar k as completed-address tick relations on the absolute clock.

Geometric phase as accumulated real-dial holonomy around a closed address loop.

The CHSH bound as balanced orthogonal-rail access geometry; the same equal-capacity rule gives Koide's sqrt 2. P_win = cos^2(pi/8).

The A1 clock-projection constant equals the T-gate magic-state overlap and the symmetric CHSH optimum; pi/8 is derived from the real-dial commutators, not assumed.

Integer flux quanta and the Josephson frequency from 2-pi modular closure of the charge dial.

Derives the complete two-sided bounded free packet sector of a finite nearest-neighbour A1 real-J dial update. With Q=-Delta/4, the unique spectral gate is P_A6=1_[0,1](Q). On its range, C=I-2Q and R=2 sqrt(Q(I-Q)) form an exact orthogonal one-tick rotor. Version 4.0 writes every integer power as U_A6^N=[[T_N(C),R U_{N-1}(C)],[-R U_{N-1}(C),T_N(C)]] and freezes the continuum residual DeltaPhi_N=N(Omega-K)=N K^3(1-sum_a n_a^4)/24+O(N K^5). Thus eta_1=0, eta_2=(1-sum_a n_a^4)/24, gamma_2=3 eta_2, and the one-rail residual vanishes exactly. The source law also prints the exact sine-squared stencil dispersion, sin^2(omega t_tilde/2) = (c_QTT t_tilde/ell_tilde)^2 sum_a sin^2(k_a ell_tilde/2), and recovers partial_T^2 theta_J - c_QTT^2 nabla^2 theta_J = 0 in the smooth limit. Because the stencil is even in k and omega, a linear Planck-scale vacuum-dispersion term is forbidden. Orthogonal maps commuting with P_A6 compose inside the free sector, but a printed counterexample shows that generic pointwise quadratic interactions do not preserve it. The nonlinear capacity completion is therefore open. A laboratory verdict also requires a separately derived source-to-field camera.

Closes the one-loop Collins percolation test for the QTT finite-address regulator class without arguing from Planck suppression. For every legal local scalar profile F(ell_A^2 k_E^2), O(4) tensor reduction gives Pi_SME^LV[Gamma_1PI^Artian-Gamma_1PI^Lorentz]_{d<=4}=0. The deliberately anisotropic control F_xi=exp[-a(k_0^2+xi|k|^2)] is carried through the same projector and gives Delta c(xi)=e^2(xi-1)/(16*pi^2) times the integral of y^2/[(1+y)^(3/2)(xi+y)^(5/2)], with Delta c(1)=0 and Delta c'(1)=alpha/(12*pi). The cutoff scale cancels, proving that the isotropic zero is a symmetry zero rather than a blind projector. The physical entire branch F(z)=exp[-H(z)] has no finite-plane zeros or new poles and is defined by Euclidean-first contour continuation, for which the paper proves perturbative Cutkosky transfer under its printed Hermiticity, convergence, BRST, and no-spurion hypotheses. Full Postulate E derivation, Osterwalder-Schrader reconstruction, strict subaddress microcausality, and dynamical gravity/lapse loops remain open.

Separates the monotone completed-history count N_rec from the laboratory-accessible memory state M_acc, so local erasure, subsystem reversal, or instantaneous-state recurrence does not delete a completed historical event. Independent record fragments obey the product law F_joint=product_k F_k. Correlated fragments instead use the Uhlmann fidelity of the full joint record states, with no universal fixed mixed-state fan-out factor claimed. The timing layer introduces a finite record-mismatch complex and its central alignment projector. A declared physical encoding W must satisfy W^dagger M_U^op W=P_align before the mathematical projector may be called an instrument observable. Observation as Access first imported this theorem in v7 and preserves it through v11.01. The companion blind test freezes an ordinary qualification stage and a QTT timing-discriminator stage over N=1,...,4, all m partitions, five fidelity corridors, holdouts, topology twins, and a second physical technology. Version 1.4 also executes 11,009 public Gosling traces with a disjoint train/guard/test split. The one-TLS Solomon camera learns two rates per trace and wins 92.37% of held-out rows, with a 36.0% median relative RMSE gain. QTT's public predata statement requires distributed record support without those fitted rates, closing a zero-fit source-explanatory victory. Because F_res, D, U_T, and W are absent, the same-observable trajectory and timing observation remain sealed and pending.

Constructs the operational object behind the Access Law rather than inferring it from a convenient laboratory residual. A coherent-survival kernel K_coh and positive unital address-centralization map Z_w give A_w(L)=I-Z_w[K_coh(L)^dagger K_coh(L)], with 0<=A_w<=I and eta=Tr(rho A_w). For a complete physical instrument, the same effect family obeys the exact identity i_A=N^-1 I(K:Q), the ceiling 0<=i_A<=N^-1 sum_j h_2(eta_j)<=h_2(eta_bar), the inherited work bound w_E<=w_R_bar+integral_[s_R-i_A]^s_R T(s)ds, and the registered uncertainty floor Delta X_j Delta P_j>=(hbar/2)(1-eta_j). The scalar-inversion no-go proves i_A!=eta in general, so work data cannot manufacture the QTT operator. The original central-projector theorem is recovered exactly when A_w^2=A_w=A_w^dagger. The 8,407-check retrospective audit gives a green structural confirmation of the state-plus-access work architecture and a zero-fit source-explanatory victory for the QTT access object. The standard information-theory identities keep their standard ownership. Version 11.01 adds a branch-resolved count-to-decision interface that separates design labels from stochastic outcomes and refuses records under one global error budget. The QTT-specific canonical same-effect cross-lock remains prospectively sealed.

Builds on the v11.01 operational central-effect constructor by requiring one authenticated laboratory access route to control two independently read consequences. For the central effect M, the normalized QTT bracket is [q,p]=J(I-M), so a closed displacement commutator has the exact operator C_QTT(phi)=M+exp(-J phi)(I-M). A symmetric binary coherent-state work arm independently measures the route weight through w_j=eta_j. On untouched loop copies the same effect then predicts R_jk=(1-eta_j)+eta_j exp(J phi_k), where ordinary quantum mechanics predicts R_jk=1 for the idle route. The five access weights, four loop areas, both loop orientations, covariance order, target-free constructor Jacobian, terminal alphabet, eligibility gates, and classifier are frozen. The work arm is standard-physics qualification rather than QTT-exclusive evidence; only the eligible full complex loop surface discriminates the theories. Version 1.0 passes three adversarial reviews and 135 of 135 deterministic release checks. Physical activation, observation, and independent replication remain pending.

Upgrades the A7U/no-pure-particle theorem into a sharper same-universe access object. The completed bundle is still the pure object: Q_w^bundle=sum_k Q_{k,w}^vis=2*pi. A finite observer sees only the access marginal rho_{S|w}^{(O)}=M rho_B M/Tr(M rho_B), with eta=Tr(rho M) and [X,P]=J hbar(I-M). The paper then defines the A7U-G finite cut-gap delta_G(Gamma)=2/N_Gamma*(1-1/N_Gamma) once the chamber boundary count N_Gamma is printed before data. The molecular transport paper then maps delta_G(Gamma_j) through T_vis into F_j^A7U and block-profiled visibility shapes. Sealed Test A asks for that nonconstant shape in one independently calibrated configuration. Separate sealed Test B closes the exact migration law v_B=Lambda_AB v_A and requires the whole fingerprint to move between two configurations while rejecting a stationary laboratory feature at five-sigma design power. Pedalino/Arndt data stay consistency-green after apparatus profiling, but direct observation remains pending because the public archive does not execute either prospectively frozen physical target.

The single-address pairwise resolution load R_n <= 2-pi forces n in {1,2,3}. The triad exactly saturates the budget (R_3 = 2-pi; R_4 = 4-pi).

The monadic / dyadic / triadic equal-share closures map to U(1), SU(2), SU(3); the e/3 charge quantum follows from the dyad-triad lattice.

After the photon house 8 and neutral projected half-loop rho/2 are quotient out, the residual five-rail edge gives alpha_QTT^-1 = 4*pi*(8 + rho/2 + lambda_gamma) = 137.035999165998, landing -0.523927 sigma against CODATA 2022 without using the observed alpha as a constructor.

NICK ladder: chi_YM = 2/3 + 1/(16 pi^2 cos^2(pi/8)) gives alpha_s = 1/(4 pi chi_YM) = 0.118052, +0.06 sigma. No observed alpha_s used.

Standard 4-loop running of alpha_s(m_Z) gives Lambda_3 = 334.65 MeV (+0.19 sigma); the A6-blocked transfer gives sqrt(sigma) = 444.25 MeV (-0.11 sigma).

Center-neutral adjoint-pair Haar transfer: m(0++)=1.731 GeV (+0.013 sigma), with tensor and pseudoscalar rows from spin-shear and odd-J exposure.

lambda_h = 1/2 + 37/(64 rho^2) gives m_h = 125.204 GeV (+0.038 sigma) as the radial vibration of the scalar-lock ruler.

The monadic U(1) address-transport theorem; Maxwell is the laboratory shadow of single-share modular transport, 1/sqrt(mu0 eps0) = c.

For a finite completed-event graph class carrying commuting molecule and surface reversals, the chirality-sector multiplicity equals the number of graph orbits whose stabilizer admits the selected character. A one-dimensional odd source sector read through one common scalar access kernel has one normalized energy shape, with sign fixed by chirality. The identity p_odd=(p_+-p_-)/2 makes nonzero opposite-sign separation a necessary-sector activation test. For a positive two-channel transmission operator Q, the vector Log-Gram decomposition log Q=alpha I+r.sigma fixes the normalized output exactly as rho_out=(I+tanh(|r|) rhat.sigma)/2. Common scalar gain cancels, basis changes rotate r without changing |r|, and commuting common-rail molecular segments add their rapidities. A declared facial defect has a signed rapidity subtraction law. For Cu(643), the independently constructed terrace line fixes D_t=I-2tt^T before the spin curves are read. The bifacial-ladder and heptahelicene rows give 25.17 and 14.38 quadrature-combined quoted-uncertainty separations under the provisional independence model; the ladder mirror-shape cosine is 0.9976 and the Cu terrace fraction is 80.98 percent. These support the joint A4-A7 dependency chain retrospectively. The four-cell molecule-by-surface design remains the prospective sector-identification test. The separately sealed molecular-length/defect protocol tests the serial Log-Gram law on raw currents; its fixed coefficient 1/[4pi cos(pi/8)] is explicitly a conjecture, not a theorem.

Closes the source-access interpretation of electromagnetic and gravitational Aharonov-Bohm phases. The compact source object is W_gamma^QTT=exp{J[(q/hbar c) int_gamma A_mu dx^mu - (mc^2/hbar) int_gamma d tau_A2]}. The first term is A4 real-J charge holonomy; the second is A2 endurance/proper-time holonomy. Version 2.0 adds the A6 phase-density gate lambda_e^AB=|delta S_e^AB|/(hbar n_e)<=1. Low-density AB experiments must recover textbook phases; only a declared high-load edge can become a QTT-specific deviation row.

Separates the frozen QCD vector-current source, the muon photon-clock kernel, and laboratory access rows for the HVP contribution to muon g-2. The source equation is a_mu^HVP = (alpha_lambda^2/3*pi^2) int K_VP(s/m_mu^2) R_src(s) d ln s, with R_src(s) = (11/3) sum_xi nu_xi chi_xi(s) and nu=(1/704)(279,31,62,9,1,2,256,64). The constructor firewall forbids a_mu^exp, lattice HVP, measured R(s), covariance packets, nuisance directions, and fitted resonance parameters from writing the source. Version 50.0 executes the BaBar publication packet with the preregistered n_B=4 access word and the published full covariance. The packet, camera, control, projection, robustness, and no-retune gates close. The scalar direction remains moderate, but the frozen resolved lineshape is rejected by the BaBar covariance row: chi2_shape is 57765.6144 or 85030.2611 for 139 degrees of freedom against the preregistered 167.5143 gate.

Closes the precision-metrology Rydberg rail as a source/lab audit rather than a fitted spectroscopy decimal. The V5.01 theorem prints the electron rank-anatomy constructor R_e^ctor=256*384*198*97=1,888,026,624, the legal gamma-W covariance door 64=2_cov*32_Sigma, the access exponent I_e=1/(rho R_e)+1/(64 R_e)=9.951823065003947e-11, the source electron mass m_e^source=0.510998950610811 MeV, and the Rydberg corridor R_infty^QTT=10,973,731.568156838 m^-1 with z_R=-0.0135 sigma. It then propagates the frozen packet into atomic units and declares real hydrogen and QED windows as no-retune audit rows. The upstream source-only SI endpoint bridge is now closed as a source/GeV ruler map and firewall, while the completed address-capacity numerical certificate remains amber. Observed R_infty, observed alpha, fitted electron corrections, Lamb/HFS data, a_e, muonium, and positronium are not allowed to write the constructor.

Builds finite nuclear magnetic-response and electronic-contact source objects, then composes them over the shared real-J scalar algebra. For one alkali line, y_ab=G_a C_b, so the observation identifies a product rather than its two source factors. Across a bipartite clock family, z=B theta and rank(B)=v-q with dim ker(B)=q for q connected components. One independent nuclear or contact source pin per component is necessary and sufficient; alternating cycles give parameter-free product locks. The first non-definitional gate is nu_87Rb/nu_133Cs=(7/6)(G_87 C_87,5s)/(G_133 C_133,6s), where the endpoint, Artian tick, Rydberg scale, alpha rail, and electron-proton mass ratio cancel. The old identity-transfer branch is rejected by a +57.296978% residual; the numerical heavy-alkali source matrices remain open.

Closes the source-only SI/GeV endpoint bridge as a legal ruler map and constructor firewall. The source chain is t_A=ell_A/c, E_* t_A=hbar, E_*=hbar c/ell_A, with SI and GeV readout rails E_*[J]=h_SI nu_*[Hz]/(2*pi) and E_*[GeV]=h_SI nu_*[Hz]/(2*pi*10^9 e_SI). The theorem forbids observed G, R_infty, electron mass, electroweak rows, alpha, or CODATA metrology comparators from writing E_* at the source layer. Its honest boundary is the remaining amber gate: a completed address-capacity numerical certificate for the absolute A5-X ruler still has to be printed without importing downstream laboratory rows. Version 3.0 closes the K2 factorization N_K2=(alpha_lambda^2/(4*pi))*(m_e^source c^2/E_*)*Phi_Cs^source and prints Phi_Cs^target=2.7942472e-6. The downstream joint-address hyperfine theorem closes finite nuclear/contact composition and proves the one-source-pin-per-connected-component identifiability condition; the numerical heavy-alkali source packet remains the active amber hinge.

Closes the narrow A6 hinge in the QCD center-sheet string-tension chain. A nonzero Z3 center boundary forces a center sheet. A local sheet crossing has exactly two sides, inside and outside, and A6 finite capacity forbids a preferred side. The unique real, capacity-preserving, unbiased transfer is the Hadamard block, giving S_A6(k=±1)=1/2. Version 4.0 then closes the declared first-order compact-color transfer class: the only legal nonconstant generator is Phi_3(U)=(1/3)Re_J Tr(U), so K_betaZ^QTT(U)=exp[(beta_Z/3)Re_J Tr(U)] is forced before the Haar readout. The comparator string tension does not choose this share, beta_Z, or kernel; it audits the already-locked source.

Uses the v4.0 forced compact-color source kernel plus the compact SU_J(3) Haar-root readout to lock c_3/c_1(beta_Z)=0.849017324821154, s_3^A6=1.76228797539733, sqrt(sigma_3)^QTT=444.25315096 MeV, and sigma_3^QTT=0.1973608621 GeV^2. The locked scale then feeds M_rho/omega^src=769.469029 MeV, M_phi^src=1025.958705 MeV, the muon-HVP centroid-compressed source weights (0.84421586, 0.09380176, 0.06198237), the rho-pipi fold-width rail, f_pi,src=90.682795 MeV, F_chi=92.038391 MeV, and glueball absolute rows m_G=r_G sqrt(sigma_3). These are source-plus-access targets, not fitted pole masses or channel fractions. The Atlas keeps the Clay smooth-continuum proof question separate from this QTT source theorem.

Derives the frozen charged-fermion integer ladder (t,b,tau,c,s,mu,d,u,e) -> (0,4,4,5,8,8,11,12,13) from the 16-sector dial, generation shell, Higgs orientation, and right-handed hypercharge residue. The integer depths are not chosen after looking at masses.

Top is the zero-depth identity channel of the charged MARIAM ladder: ell_t = 0 and T_hat_t = 1. The native anchor is m_t^A = E_H^lab = 174.103584824 GeV; collider-direct, pole, and MS-bar readings require an explicit observation map.

Sets the charged-fermion mass target m_f(mu_obs) = E_H^lab exp(-ell_f) T_hat_f R_f, with the same depth rule, determinant-torsion functor, and QED/QCD boundary transport logic for all nine charged fermions. The depth and transport spine is clean; the all-nine exact-mass theorem waits for determinant torsions and declared scheme windows.

Closes a declared finite Artian/MARIAM constructor class for the charged-lepton family. The v3.7 source-word scan starts with 288 candidate words and leaves one survivor before measurement is opened: signs (+,-,-) and ranks (N_e,N_mu,N_tau)=(1,888,026,624,17,526,2,347). The subsequent laboratory audit gives e +0.072 sigma, mu +0.188 sigma, tau -0.046 sigma, and chi^2=0.042. This blocks the three-Yukawa free-input route inside the declared class; global uniqueness outside that class remains open.

Registers the conditional LIA neutrino family-rank identity without using oscillation gaps as inputs. Once the source vector (m1,m2,m3)=m_Delta*(0,1,rho_nu)/sqrt(rho_nu^2-1) is supplied, Delta m^2_31 / Delta m^2_21 = rho_nu^2 = 4*pi^2*cos^2(pi/8) = 33.69693720145647... follows exactly. The v1.1 neutral-branch audit closes common-factor cancellation: common completed-bundle and A1 factors do not themselves create a relative rho_nu. A finite asymmetric source pair and the five-fold neutral completion remain amber construction gates. The absolute scale m_Delta, SI-ruler, PMNS, endpoint, cosmology, and G-style rows remain observation-last audits until m_Delta is derived from an independent non-oscillation QTT source rail.

Defines the PMNS source object as the real-J relative orientation U_PMNS^src=(U_E^src)^{T_J}U_nu^src between the charged-lepton family basis and the neutral LIA basis. Version 5.0 preserves the finite first-order angle-word enumeration: |L_PMNS^(1)|=36 and exactly one active source survivor remains after source gates. It gives sin^2 theta12=0.306880189272, sin^2 theta13=0.022257215708, sin^2 theta23=0.557296543843, delta_PMNS=pi, and J_PMNS=0. The CKM micro-provenance bridge is now printed as a source certificate, while the atmospheric-octant branch, CP-profile likelihood row, and Majorana/access rows remain live falsifiers.

Makes the current quark-sector source/access framework explicit: a finite quark source complex, up/down mass sheets D_U=diag(m_u,m_c,m_t) and D_D=diag(m_d,m_s,m_b), and CKM as a path-ordered real-J holonomy V=R_23 R_13^J R_12 between sheets. Version 4.0 prints the seven-slot precision packet (20,10,104,6,7,12,192), closes the finite CKM source-word enumeration and precision micro-provenance, and leaves the global CKM covariance packet, quark-mass source-word compiler, and baryon/proton unlock pending.

Uses the closed top self-scale anchor, MARIAM depths ell_b = 4 and ell_c = 5, normalized heavy-triad torsions, QTT Yang-Mills transport, and the single-kernel QED window to predict m_b(m_b) = 4.178774016 GeV and m_c(m_c) = 1.271731720 GeV.

Closes the light u,d,s quark masses at 2 GeV with ell_s = 8, ell_d = 11, ell_u = 12, projected-loop torsion actions, common QTT YM transport, and the single-kernel QED window: m_u = 2.156580919 MeV, m_d = 4.704302901 MeV, m_s = 93.790027048 MeV.

Reads bottom/charm as a top-anchored torsion-amplitude triad, not an isolated two-body ratio. The MARIAM phase is phi_Q = -pi/104; with the QCD and photon readout gates the self-scale ratio becomes m_b/m_c = 3.28589273276, a green sigma pass in the book audit.

Reads CKM as a source-sheet holonomy inside the quark reference framework. The v4.0 precision packet gives s12=0.225042858584379, s23=0.042713531540749, s13=0.003708134796885, delta=1.147687258136975, and the left-access CKM matrix after a unique survivor is selected from 3^7=2187 finite packets. The largest row-level entry pull is about 0.28 sigma; the correlated global CKM covariance packet remains pending.

Accepts the flat w-glued Yukawa triangle as the pre-mass birth ledger and rejects disconnected direct-sum MARIAM blocks as an all-nine mass theorem. The next legal object is a coupled w-glued MinCap complex with printed spectra before mass comparison.

From capacity-quantized space plus the UEL: the Einstein equations emerge in the local Einstein gauge from the endurance current and Artian measure.

The Einstein-Hilbert coefficient forced by A2 through the endurance law; numerically the Planck-unit form, but derived prior to it (identical-equation, non-equivalent-theory).

The Lambda branch is consolidated as a Creation Ledger: late-time acceleration is read as an A3 projection effect, the exact vacuum identity is separated from fitted dark-energy fluid language, and epsilon remains a printed ledger-side IOU/falsifier.

Consolidates the dark-matter branch as fixed-coefficient source-kernel gravity: acceleration knee a0_tau = c H_tau/(2 pi), lab floor a0_tau/cos(pi/8), Renewal Dust/lensing readouts, cosmic-dipole reading, and a declared falsifier ledger. The RAR comparison is displayed as a stress row, not promoted into a green sigma claim.

The two-clock projection splits early- and late-time Hubble readouts: sec(pi/8) = 1.0824, matching the SH0ES/Planck ratio at -0.11 sigma under the Atlas convention: QTT minus observed over sigma. S4 remains open: epoch assignment and environment split must stay declared, not absorbed into a dark-energy fit.

The 18-lock 18 Omega_b^ABC (H_tau T0)^2 ~= 1; the lab projection uses Omega_b^lab = (1/18)(63.493001/67.36)^2 = 0.04935999 and is audited against the Planck physical-density row at about +0.18 sigma. The rounded 63.5/67.4 shorthand is not used for the pull.

Baryon-ledger time-drift gives an absolute 15.4 Gyr age, observed as 13.81 Gyr through the same two-clock projection.

The electro-optic Kerr constant as a finite-capacity birefringence readout of the Artian substrate.

The typed Second Law is the positive-cone pair (k_B Delta N_rec, Sigma_acc): A1/A7 supply completed-record order and persistence, while lawful physical access supplies non-negative distinguishability loss. A2 support and A3 source volume are separately derived and are not entropy increments.

Version 4.0 closes the gravity-side finite-current theorem and the conditional infrared implication without hiding its population gates. The derivation begins with B=M/m_A and dN_sink/dT=B/t_tilde, proves finite internal-edge cancellation and Ward transfer, and obtains the Newton family div(g)=-4*pi*chi_g*G_A*rho_lab with G_A=ell_tilde^2*c^3/hbar and G_end=chi_g*G_A. Opposite-pair moments eliminate odd derivatives and select a two-derivative leading infrared operator. All remaining source-to-metric obligations are carried by R_rec=Delta_C3+Delta_T+Delta_Ward+Delta_def+Delta_gain+Delta_(4). When chi_g=1 and R_rec=0, the declared metric-domain uniqueness gate forces G_mu_nu+Lambda_A3*g_mu_nu=(8*pi*G_A/c^4)T_mu_nu^A2. A constructive counterfamily proves that A6/A7 finite fixed capacity and closure per address do not alone choose chi_g=1. Thus the implication is green in its declared camera, while universal gain, C3 metric reconstruction, ABC-clock decoupling, routing covariance, and horizon saturation population remain explicit amber gates. The smooth equation is the infrared readout, not QTT source ontology.

Closes the source-side information ledger for black holes by treating the horizon as a visible/hidden access cut through one completed A7 bundle, not as an ontological destruction channel. Version 4.0 also closes the Bekenstein quarter without a Hawking constructor: Q_Sigma=8*pi*ell_tilde^2, N_H=A/(4*ell_tilde^2), and S_H^QTT=k_B*A/(4*ell_tilde^2), with 1/4=2pi/8pi. The laboratory outside state is rho_vis=Tr_hid rho_src and may be thermal or mixed, while the completed source state follows a source-unitary A7 transfer rho_src(T2)=U_A7 rho_src(T1) U_A7^dagger. T_eff=hbar*kappa_s/(2*pi*k_B*c) is a first-law/access readout after entropy is fixed; Hawking radiation is rejected as a source constructor. A6 finite capacity denies an infinite source singularity or required remnant, and the future Page-envelope row is S_rad^fine(T) <= min(S_emitted(T), S_remaining(T)) with t_Page/t_drain=1-1/(2*sqrt(2)). Species-resolved S-matrix and thermal-flux population remain access-test rows, not claimed observed sigmas.

Prints three blind no-retune source-access tests for A2 endurance holonomy. The discriminator is not the ordinary gravitational phase: the blinded pair must satisfy Theta_IR(P_A)=Theta_IR(P_B) while the finite A2 source packets differ, A_A2(P_A)!=A_A2(P_B). The packet records edges, A2 action spends, completed tick counts, phase-density loads, lab covariance, and the source/access window. Test 1 is an equal-action/unequal-load gravitational AB chopper; Test 2 is the echo-cancelled endurance covariance row; Test 3 is a frontier quantum-source holonomy witness without a source graviton.